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Homework Help: Problems with Electric Field questions

  1. Mar 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the point on the x-axis where the net electric field is zero for two particles of charges q1=1x10^-9C and q2=2x10^-9C. Assume q1 and q2 are 20cm apart. Assume q1 is located at x=0.

    I solved this but it's not the same as the book's answer.. GAH! What do you guys get? Thanks.

    2. Relevant equations
    Enet=E1+E2, Enet=0 => |E1|=|E2|

    E=kq/r² where q is the charge creating the field

    3. The attempt at a solution
    E1=kq1/r²
    E2=kq2/(.2m - r)²

    kq1/r²=kq2/(.2m - r)²
    q1/r²=q2/(.2m - r)²
    q1(.2m - r)²=q2r²
    q1(.2m - r)²=q2r²
    q1(0.4m-0.4mr+r²)-q2r²=0 <------ There's my mistake
    (q1)0.4m-(q1)0.4mr+(q1)r²-q2r²=0
    (q1-q2)r²-(q1)0.4mr+(q1)0.4m=0
    ((1E-9C)-(2E-9C))r²-(1E-9C)0.4mr+(1E-9C)0.4m=0
    (-1E-9C)r²-(1E-9C)0.4mr+(1E-9C)0.4m=0
    (-1E-9C)r²-(4E-10C)mr+(4E-10C)m=0
    (-1E-9)r²-(4E-10)r+(4E-10)=0
    r=-0.863325 or r=0.463325

    The answer in the book is 8.3cm. Where did I go wrong?
    ------
    Edit:
    q1(.2m - r)²=q2r²
    q1(0.04m-0.4mr+r²)-q2r²=0
    (q1)0.04m-(q1)0.4mr+(q1)r²-q2r²=0
    (q1-q2)r²-(q1)0.4mr+(q1)0.04m=0
    ((1E-9C)-(2E-9C))r²-(1E-9C)0.4mr+(1E-9C)0.04m=0
    (-1E-9C)r²-(1E-9C)0.4mr+(1E-9C)0.04m=0
    (-1E-9C)r²-(4E-10C)mr+(4E-11C)m=0
    (-1E-9)r²-(4E-10)r+(4E-11)=0
    Positive r comes out to 8.3cm
     
    Last edited: Mar 13, 2008
  2. jcsd
  3. Mar 13, 2008 #2
    do you realise that Q2 has charge two times of Q1? Simply suibstitute Q2 with 2Q1 and cancel out the Q1s and your equations will appear much simpler.




    I managed to simplify the equation into a quadratic equation offhand. You should arrive at a quadratic equation.
     
    Last edited: Mar 13, 2008
  4. Mar 13, 2008 #3
    Right, you can see:

    (-1E-9)r²-(4E-10)r+(4E-10)=0 before I found my mistake and
    (-1E-9)r²-(4E-10)r+(4E-11)=0 after I found my mistake.

    Those are quadratic equations.
     
  5. Mar 14, 2008 #4
    to tell you the truth, I was actually too lazy to go through those equations. It was a pain for my eyes hah.

    But the point is if you know that your steps were correct, that means somewhere along the line you had a simple miscalculation.
     
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